If you drive through the beautiful Perche region, between the towns of Mortagne-au-Perche and Belleme is the wonderful restaurant La Croix d'or in tiny Le pin la garenne. This is our favorite restaurant in the Perche, warmly welcoming, affordable, and delicious. Check that it is open on the day and at the time you plan to pass through. You would need reservations.
Farther south on the same route is Du dauphin in La Ferte Bernard. Excellent food and quiet and attentive service. Check their website for open days and hours. I recommend reservations.
If you have time, a walk around Mortagne, Belleme, or La Ferte Bernard would give you a pleasant break and a look at some architectural gems. The Perche is known for its stone manor houses of the 15th-16th century, some of which you can see on a drive down some country roads.
Recently someone here highly recommended a particular restaurant in Alencon, which caught my interest and we plan to try it on our next visit, but I'll let him give you the name, which I made a note of at the time but can't recall at the moment.
R10, the little blue ice cream shop across from the church doors in Mortagne has the best ice cream I've ever tasted. Their hours change so it's not easy to time a visit right, but I wanted you to know about it just in case.